Screening the arms and leads of a precision alternating bridge serves to
Answer: C
Stray capacitance cannot be abolished, but earthed screens fix it at a value that does not change when the operator moves a hand near the apparatus. Once definite, it can be balanced out or calculated, whereas a wandering stray defeats any precision.
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Residuals in a bridge arm mean
Answer: D
A wire-wound resistor has self inductance and self capacitance, and a capacitor has lead inductance and dielectric loss. At audio frequencies these residuals are small but not negligible, and precision work either allows for them or uses arms specially constructed to minimise them.
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Mutual inductance between the arms of a bridge is troublesome because it
Answer: A
Flux from one arm linking another adds an unaccounted term to the balance equation. The remedies are to space the coils well apart, to set them with their axes at right angles, and to screen them, which is one more reason capacitance standards are preferred to inductance standards.
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A Maxwell-Wien bridge balances with \( R_2 = 1000\ \Omega \), \( R_3 = 500\ \Omega \) and \( C_4 = 0.5\ \mu \)F. Using \( L_1 = R_2 R_3 C_4 \), the unknown inductance is
Answer: B
Substituting gives \( 1000 \times 500 \times 0.5 \times 10^{-6} = 0.25 \) henry. Notice that the frequency does not appear, so this bridge gives the inductance without the supply frequency needing to be known or held steady.
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In the same Maxwell-Wien bridge, with \( R_4 = 10\ \)k\( \Omega \) and \( R_1 = R_2 R_3 / R_4 \), the resistance of the coil is
Answer: C
The arithmetic is \( 1000 \times 500 / 10000 = 50\ \Omega \). Both parts of the balance come from the same set of readings, so a single balance yields the inductance and the resistance of the coil together, and from them its quality factor.
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A coil of 0.25 H and 50 \( \Omega \) is measured at 50 Hz. Its quality factor is about
Answer: D
The reactance is \( 2\pi \times 50 \times 0.25 = 78.5\ \Omega \), so \( Q = 78.5/50 = 1.57 \). A quality factor near unity is a lossy coil, and it is for coils of this kind that the Maxwell-Wien and Anderson bridges are suited rather than Hay's bridge.
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In Hay's bridge \( Q = 1/(\omega C_4 R_4) \). With \( C_4 = 0.5\ \mu \)F, \( R_4 = 100\ \Omega \) and a frequency of 1 kHz, the quality factor of the coil is about
Answer: A
The denominator is \( 2\pi \times 1000 \times 0.5 \times 10^{-6} \times 100 = 0.314 \), and its reciprocal is 3.18. Since Q here is only about three, Hay's bridge would introduce an appreciable error in the inductance and another form would be preferred.
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A Wien bridge uses \( R = 10\ \)k\( \Omega \) and \( C = 0.01\ \mu \)F in its frequency-determining arms. With \( f = 1/(2\pi RC) \) the balance frequency is about
Answer: B
The product \( RC \) is \( 10^4 \times 10^{-8} = 10^{-4} \) second, and dividing that into \( 1/2\pi \) gives about 1592 hertz. The same network, placed round an amplifier, fixes the frequency of the Wien bridge oscillator.
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A Schering bridge at 50 Hz balances with \( C_4 = 0.5\ \mu \)F and \( R_4 = 637\ \Omega \). Using \( \tan\delta = \omega C_4 R_4 \), the dissipation factor of the specimen is about
Answer: C
The angular frequency is 314.2 radians per second, and \( 314.2 \times 0.5 \times 10^{-6} \times 637 = 0.100 \). A loss tangent of a tenth is high for sound insulation, where a few thousandths would be usual, so such a specimen would be viewed with suspicion.
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If the dissipation factor of a specimen measured on a Schering bridge is 0.04 at 50 Hz, then at 100 Hz with the same arm settings the bridge would indicate
Answer: D
The expression \( \tan\delta = \omega C_4 R_4 \) is directly proportional to frequency, so with the arms unchanged the indication doubles. This is why the test frequency must always be quoted alongside a loss tangent, and why readings at different frequencies cannot be compared directly.
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